两个点到根节点的距离 - lca到根节点的距离 * 2

#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long LL;
const int N = 4e4+10,M = N * 2;
int n,m;
int h[N],e[M],ne[M],w[M],idx;
int fa[N][16];
int depth[N];
int dist[N];
queue<int> q;

void add(int a,int b,int c)
{
    e[idx] = b,w[idx] = c,ne[idx] = h[a],h[a] = idx++;
}

void bfs(int root)
{
    memset(depth,0x3f,sizeof depth);
    depth[0] = 0,depth[root] = 1;
    q.push(root);

    while(q.size())
    {
        int t = q.front();
        q.pop();

        for(int i = h[t];~i;i = ne[i])
        {
            int j = e[i];
            if(depth[j] > depth[t] + 1)
            {
                depth[j] = depth[t] + 1;
                dist[j] = dist[t] + w[i];
                q.push(j);
                fa[j][0] = t;
                for(int k = 1;k<=15;k++)
                {
                    fa[j][k] = fa[fa[j][k-1]][k-1];
                }
            }
        }
    }
}

int lca(int x,int y)
{
    if(depth[x] < depth[y])swap(x,y);
    for(int k = 15;k>=0;k--)
    {
        if(depth[fa[x][k]] >= depth[y])
        {
            x = fa[x][k];
        }
    }

    if(x == y)return x;

    for(int k = 15;k>=0;k--)
    {
        if(fa[x][k] != fa[y][k])
        {
            x = fa[x][k];
            y = fa[y][k];
        }
    }
    return fa[x][0];
}

int main()
{
    memset(h,-1,sizeof h);
    cin>>n>>m;
    int root;
    for(int i = 0;i<n-1;i++)
    {
        int a,b,k;
        cin>>a>>b>>k;
        add(a,b,k),add(b,a,k);
    }

    bfs(1);

    while (m -- )
    {
        int x,y;
        cin>>x>>y;
        int p = lca(x,y);
        cout<<dist[x] + dist[y] - 2 * dist[p]<<endl;
    }

    return 0;
}

dfs版本

#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long LL;
const int N = 4e4+10,M = N * 2;
int n,m;
int h[N],e[M],ne[M],w[M],idx;
int fa[N][16];
int depth[N];
int dist[N];
queue<int> q;

void add(int a,int b,int c)
{
    e[idx] = b,w[idx] = c,ne[idx] = h[a],h[a] = idx++;
}


void dfs(int u,int f)
{
    depth[u] = depth[f] + 1;
    fa[u][0] = f;

    for(int i = 1;i<16;i++)
    {
        fa[u][i] = fa[fa[u][i-1]][i-1];
    }
    for(int i = h[u];~i;i = ne[i])
    {
        int j = e[i];
        if(j == f)continue;
        dist[j] = dist[u] + w[i];
        dfs(j,u);
    }
}

int lca(int x,int y)
{
    if(depth[x] < depth[y])swap(x,y);
    for(int k = 15;k>=0;k--)
    {
        if(depth[fa[x][k]] >= depth[y])
        {
            x = fa[x][k];
        }
    }

    if(x == y)return x;

    for(int k = 15;k>=0;k--)
    {
        if(fa[x][k] != fa[y][k])
        {
            x = fa[x][k];
            y = fa[y][k];
        }
    }
    return fa[x][0];
}

int main()
{
    memset(h,-1,sizeof h);
    cin>>n>>m;
    int root;
    for(int i = 0;i<n-1;i++)
    {
        int a,b,k;
        cin>>a>>b>>k;
        add(a,b,k),add(b,a,k);
    }

    dfs(1,0);

    while (m -- )
    {
        int x,y;
        cin>>x>>y;
        int p = lca(x,y);
        cout<<dist[x] + dist[y] - 2 * dist[p]<<endl;
    }

    return 0;
}